agreed that the lack of filesystem exposed to the user is one of the most striking desktop PC metaphors omitted from iOS. at least for someone who understands filesystems. I'm the kind of person that used to hand-curate my mp3 collection according to very a specific file naming scheme. you probably are too. (now I'm pretty happy to let iTunes do that.) my coworkers' computers, on the other hand, have APPALLING desktops. piles and piles of files and folders, so buried that they can't find anything, yet that's where they habitually continue to save every file they collect, despite my having shown them how to make their browsers download to other folders by default, etc. the smarter among them have fallen back on exclusively using the search feature in file picker dialogs to find files they can't remember where they saved. (so pretty much everything.)
having used both Android and iOS, Android apps seem to be pretty messy with where they store files. iOS apps might be too, but I couldn't tell, so at least it didn't bother me. as other commenters have noted, the example of the Photo Library is a model that could be extended for passing other kinds of files between apps.
iOS doesn't show a filesystem to the user because it was designed for my coworkers. I think Apple made the right choice. it's one of the things that makes iOS feel unlike a computer, that liberation from the hopelessly disorganized desktop and home folders that most people can't help but spawn.